SIMON FRASER UNIVERSITY
DEPARTMENT OF MATHEMATICS
Midterm 2
MATH 232 Fall 2010
Instructor: Prof. JF Williams
Nov. 12 2010, 11:30 12:20
Name:
(please print)
family name
given name(s)
student number
@sfu.ca e-mail
SFU IDs:
Signature:
Instructions:
1. Do not
Solutions to Math 232 Final, Version 1 (Blue/Grey)
Spring 2012, Simon Fraser University
1(a).
5 2 1
5 4 1
10 2 2
1 0 = 2
2 3
A + AT = 4 1 3 + 2
1 03
1
33
2
36
1(b). det(B ) = (1)(2)(1) = 2 (the product of the diagonal entries) since
B is upper triangular.
Solution Set, Math 232 Midterm 2, Version 1
(Green/Grey)
Spring 2012, Simon Fraser University
1(a).
k
ij
u v = 1 5 2
2 0 3
= 15 + + 10k
ij
1(b).
(u u) v = 0 v
=0
where the rst step uses the fact that cross product of two parallel vectors
is the zero vecto
Final exam: Math 232
GREEN SOLUTIONS
Instructions/Remarks:
Read all instructions.
The questions are on the 12 numbered single-sided pages following this one. Count them now.
Please include all details and rough work. You may use the back of the questio
SIMON FRASER UNIVERSITY
DEPARTMENT OF MATHEMATICS
Midterm 1
MATH 232 Fall 2011
Instructor: Prof. JF Williams
Oct. 7 2011, 11:30 12:20
Name:
(please print)
family name
given name(s)
student number
@sfu.ca e-mail
SFU IDs:
Signature:
Instructions:
1. Do not
(a) Find the gradient of
Vcfw_ =
/ at the ,rr^, 6:?j
<#, #,"4 >= I e"a;o, *3o, 2 rTe >
= (.2.,
l) rl >
(b) Find the equation'of tangent plane to the isotimic surface
at the point (0,2,
I:
2,
1)
[=12rrr?2 ->
zcr-q t tC*2)r?(A-D:,Q
.5
-/ zrr7r ?5=6
(c) Find
120
This version: 22/10/2004
4 Frequency response (the frequency domain)
22/10/2004
by
= cfw_ R | i is a pole of T .
The frequency response for is the function H : R\ C dened by H () = T (i).
Note that we do wish to think of the frequency response as a
Exam Name (please print) 7/
Math 332 Fall 2012. November 1, 2012
Show work and correct notation for full credit!!! Give numerical or simple fraction
answers whenever possible.
Problem l 1 2
Earned i
37 4 lTotall
Possib